I teach a graduate seminar almost every spring semester, Moral Emotions and Resistance, that explores a spectrum of emotions, starting with despair and ending with forgiveness. I think, perhaps surprisingly, that both apathy and hate are valuable moral attitudes—although they’re not without limitations.
 
Apathy and hate often arise in response to wrongdoing. One might feel apathetic about climate change or hate politicians they see as causing harm. In this context, both emotions can serve to protect someone who is a victim of or witness to wrongdoing. Apathy allows one to rest from the constant onslaught of loss, injustice, and trauma in the news cycle or, possibly, one’s own life. Hate, on the other hand, comes from and stokes an anger that can demand justice by asserting one’s rights, existence, and importance. Hate aims to hold wrongdoers accountable. 

That said, both can be problematic if they become chronic. Apathy can not only deter one from acting, but also cause one to withdraw and become alienated from their community and even themselves. Hate can also be destructive to communities and can even have a deleterious impact on one’s health. 
 
It’s not a matter of which negative emotion is worse—neither gets the attention it deserves. The real question is how to attend to their potential value.